Early Warning Signs of an Unusual Mentor
Carl Boettiger
07/28/2014
from the hair

from the recumbant

from the Hawaiian shirts

From the jokes that never got old …
… That Alan would be an unusual advisor
Advising styles

Advising styles

A growing literature on early warning signals

Alan Hastings, Everyone’s favorite skeptic

Alternative states


Alternative stable states


Tipping points


They have happened in the past


will they happen again?

Are there warning signs?

credit: A. Hastings
A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

A mechanism for state shifts

Without controls
All we have is a squiggle

All we have is a squiggle

Making predictions from squiggles is hard
EWS or Squiggle?

Underlying model?
There’s always an underlying model!

Underlying model? There’s always an underlying model!
Say that in math. Canonical form of approaching saddle-node bifurcation:
\[d X = \sqrt{ r_t } (\phi(r_t) - X_t)d t + \sigma\sqrt{\phi(r_t) } d B_t\]
Underlying model? There’s always an underlying model!
Solve for the moments:
\[\frac{d }{d t} E(x| M) = f(x)\]
\[\frac{d}{d t} V(x| M) = -\partial_x f(x) V(x|M) + g(x)^2\]
Advantages
- Avoids sliding window fallacy
- (non-independence, non-stationarity, abitrary choice of window)
- Avoids uniform spacing requirement / interpolation fallacy
- Easy compare between statistics
- Increased statistical power
- Estimate error rates
- Makes assumptions explicit
Challenges
- Assumes a saddle-node bifurcation or stable node dynamics
- Non-Bayesian: harder to update or reflect prior assumptions
- Still must define the (one-dimensional) “system state”
- Still data intensive
Prosecutor’s Fallacy

Carver, from NERSC, DOE
Charted and uncharted territories

Establishing baselines
- Statistically (ROC curves, Bayesian)
- Emprically (How do we prepare/correct data? Seasonality etc?)
Context-specific information
- Use all of the data.
- Qualitative context can guide intuition about the likely bifurcation dynamics
- Multi-dimensional warning signals
Alan Hastings, Everyone’s favorite skeptic

Gov Jerry talks about Alan’s work

Gewin 2014 10.1038/511402a (photo by Justin Sullivan/Getty)